1. Mark has the same height as John.
2. Mark is the same height as John.
3. When I rode my bike, my sister drew <a href="http://www.ntsearch.com/search.php?q=pictures&v=56">pictures</a> on the road yesterday.

1. Mark has the same height as John.2. Mark is the same height as John.3. When I rode my bike, my sister drew <a href="http://www.ntsearch.com/search.php?q=pictures&v=56">pictures</a> on the road yesterday.

We refer to height using 'be', not 'have', because we are originally saying e.g. 'He IS one 1.89m TALL' (with complemental adjective 'tall' premodified by NP 1.89m). So even when using the noun 'height' in place of the measurement phrase, e.g. in 'What height are you?', the verb 'be' continues to be used under the influence of the original sentence.